Attorney General Eric Holder said Wednesday night the Justice Department would launch an “independent, thorough, fair, and expeditious” civil-rights probe into the death of Eric Garner, after a grand jury declined to indict a New York City police officer who allegedly applied a fatal choke hold.

The Justice Department had already been monitoring the local investigation of the case. Mr. Holder’s department is also conducting a criminal civil-rights probe of the officer who shot 18-year-old Michael Brown in Ferguson, Mo. A...